STABILITY OF SWITCHED POLYNOMIAL SYSTEMS

This paper investigates the stability of （switched） polynomial systems. Using semi-tensor product of matrices, the paper develops two tools for testing the stability of a （switched） polynomial system. One is to convert a product of multi-variable polynomials into a canonical form, and the other is an easily verifiable sufficient condition to justify whether a multi-variable polynomial is positive definite. Using these two tools, the authors construct a polynomial function as a candidate Lyapunov function and via testing its derivative the authors provide some sufficient conditions for the global stability of polynomial systems.     

Strong Law of Large Numbers for Weighted Sums of Random Variables and Its Applications in EV Regression Models

This paper mainly studies the strong convergence properties for weighted sums of extended negatively dependent(END, for short) random variables. Some sufficient conditions to prove the strong law of large numbers for weighted sums of END random variables are provided. In particular, the authors obtain the weighted version of Kolmogorov type strong law of large numbers for END random variables as a product. The results that the authors obtained generalize the corresponding ones for independent ra...     

Generating semi-algebraic invariants for non-autonomous polynomial hybrid systems

Hybrid systems are dynamical systems with interacting discrete computation and continuous physical processes, which have become more common, more indispensable, and more complicated in our modern life. Particularly, many of them are safety-critical, and therefore are required to meet a critical safety standard. Invariant generation plays a central role in the verification and synthesis of hybrid systems. In the previous work, the fourth author and his coauthors gave a necessary and sufficient condition for a semi-algebraic set being an invariant of a polynomial autonomous dynamical system, which gave a confirmative answer to the open problem. In addition, based on which a complete algorithm for generating all semi-algebraic invariants of a given polynomial autonomous hybrid system with the given shape was proposed. This paper considers how to extend their work to non-autonomous dynamical and hybrid systems. Non-autonomous dynamical and hybrid systems are with inputs, which are very common in practice; in contrast, autonomous ones are without inputs. Furthermore, the authors present a sound and complete algorithm to verify semi-algebraic invariants for non-autonomous polynomial hybrid systems. Based on which, the authors propose a sound and complete algorithm to generate all invariants with a pre-defined template.     

Generating exact nonlinear ranking functions by symbolic-numeric hybrid method

This paper presents a hybrid symbolic-numeric algorithm to compute ranking functions for establishing the termination of loop programs with polynomial guards and polynomial assignments. The authors first transform the problem into a parameterized polynomial optimization problem, and obtain a numerical ranking function using polynomial sum-of-squares relaxation via semidefinite programming (SDP). A rational vector recovery algorithm is deployed to recover a rational polynomial from the numerical ranking function, and some symbolic computation techniques are used to certify that this polynomial is an exact ranking function of the loop programs. At last, the authors demonstrate on some polynomial loop programs from the literature that our algorithm successfully yields nonlinear ranking functions with rational coefficients.     

Rational general solutions of higher order algebraic odes

This paper generalizes the method of Ngô and Winkler (2010, 2011) for finding rational general solutions of a first order non-autonomous algebraic ordinary differential equation (AODE) to the case of a higher order AODE, provided a proper parametrization of its solution hypersurface. The authors reduce the problem of finding the rational general solution of a higher order AODE to finding the rational general solution of an associated system. The rational general solutions of the original AODE and its associated system are in computable 1-1 correspondence. The authors give necessary and sufficient conditions for the associated system to have a rational solution based on proper reparametrization of invariant algebraic space curves. The authors also relate invariant space curves to first integrals and characterize rationally solvable systems by rational first integrals.     

Flocking with General Local Interaction and Large Population

This paper studies a flocking model in which the interaction between agents is described by a general local nonlinear function depending on the distance between agents. The existing analysis provided sufficient conditions for flocking under an assumption imposed on the system's closed-loop states; however this assumption is hard to verify. To avoid this kind of assumption the authors introduce some new methods including large deviations theory and estimation of spectral radius of random geometric graphs. For uniformly and independently distributed initial states, the authors establish sufficient conditions and necessary conditions for flocking with large population. The results reveal that under some conditions, the critical interaction radius for flocking is almost the same as the critical radius for connectivity of the initial neighbor graph.     

ON VECTOR NETWORK EQUILIBRIUM PROBLEMS

1 Introduction The earliest network equilibrium model was proposed by Wardrop (1952) for a transportation network Since then, many other equilibrium models have also been proposed in the economics literature (see Nagurney 1993) Until only recently, all these equilibrium models are based on single cost or utility function Recently, equilibrium models based on multicriteria consideration or vector-valued cost functions have been proposed In Chen and Yen (1993), a multicriteria traffic equilibr…     

OPTIMALITY CONDITIONS AND DUALITY THEOREMS IN NONCONICAL MULTIOBJECTIVE PROGRAMMING

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Controllability of Quantum Systems with SU(1, 1) Dynamical Symmetry

This paper presents sufficient and necessary conditions for the propagator controllability of a class of infinite-dimensional quantum systems with SU(1, 1) dynamical symmetry through the isomorphic mapping to the non-unitary representation of SU(1, 1). The authors prove that the elliptic condition of the total Hamiltonian is both necessary and sufficient for the controllability and strong controllability. The obtained results can be also extended to control systems with SO(2, 1) dynamical symmetry.     

QUANTITATIVE PROPERTIES OF GREEN EQUIVALENCES ON SPECIAL MONOIDS

ＱＵＡＮＴＩＴＡＴＩＶＥＰＲＯＰＥＲＴＩＥＳＯＦＧＲＥＥＮＥＱＵＩＶＡＬＥＮＣＥＳＯＮＳＰＥＣＩＡＬＭＯＮＯＩＤＳＷＵＪｉｎｚｈａｏ（ＩｎｓｔｉｔｕｔｅｏｆＳｙｓｔｅｍｓＳｃｉｅｎｃｅ，ＡｃａｄｅｍｉａＳｉｎｉｃａ，Ｂｅｉｊｉｎｇ１０００８０，Ｃｈｉ...     

Rational Solutions of High-Order Algebraic Ordinary Differential Equations

This paper considers algebraic ordinary differential equations(AODEs) and study their polynomial and rational solutions. The authors first prove a sufficient condition for the existence of a bound on the degree of the possible polynomial solutions to an AODE. An AODE satisfying this condition is called noncritical. Then the authors prove that some common classes of low-order AODEs are noncritical. For rational solutions, the authors determine a class of AODEs, which are called maximally comparable, such that the possible poles of any rational solutions are recognizable from their coefficients. This generalizes the well-known fact that any pole of rational solutions to a linear ODE is contained in the set of zeros of its leading coefficient. Finally, the authors develop an algorithm to compute all rational solutions of certain maximally comparable AODEs, which is applicable to 78.54% of the AODEs in Kamke's collection of standard differential equations.     

Periodic Solution and Ergodic Stationary Distribution of Stochastic SIRI Epidemic Systems with Nonlinear Perturbations

This paper formulates two stochastic nonautonomous SIRI epidemic systems with nonlinear perturbations. The main aim of this study is to investigate stochastic dynamics of the two SIRI epidemic systems and obtain their thresholds. For the nonautonomous stochastic SIRI epidemic system with white noise, the authors provide analytic results regarding the stochastic boundedness, stochastic permanence and persistence in mean. Moreover, the authors prove that the system has at least one nontrivial positive T-periodic solution by using Lyapunov function and Hasminskii's theory. For the system with Markov conversion, the authors establish sufficient conditions for positive recurrence and existence of ergodic stationary distribution. In addition, sufficient conditions for the extinction of disease are obtained. Finally, numerical simulations are introduced to illustrate the main results.     

复杂环境下的UWB脉冲成形算法

针对超宽带定位系统在多用户和弱信号环境下接收端易出现码间串扰(inter symbol interference, ISI)和多用户干扰(multiuser interference, MUI)等问题,提出一种基于修正最小均方误差估计(minimum mean square error estimation, MMSE)的自适应迭代算法进行超宽带(ultra wideband,UWB)脉冲设计。该算法选取修正Hermite多项式(modefied Hermite polynomial, MHP)作为脉冲设计基函数。通过分析MHP的时频特性对最小均方误差估计准则下组合脉冲的各阶MHP系数进行修正,在此基础上根据组合脉冲功率谱密度与美国联邦通讯委员会(federal communications commission, FCC)辐射掩蔽之间的拟合程度设计自适应算法,对组合脉冲进行自适应调整实现脉冲设计。仿真结果表明该方案获得的脉冲有较高功率利用率,同时在多用户接入和弱信号检测方面也具备很强的适用性。     

Optimality and Duality for Nondifferentiable Multiple-Objective Optimization with Generalized Univexity

1　 IntroductionFor the following nonlinear programming problem( P) min f( x)subjectto　　 g( x) 0　　If there exists a vector functionη( x,x0 ) such thatf( x) -f( x0 ) [ f( x0 ) ] Tη( x,x0 )-g( x0 ) [ g( x0 ) ] Tη( x,x0 )for all x,x0 ∈ S={x|g( x) 0 },then,f( x) and g( x) are said to type objective and type constraint functions[1 ] .Hanson and Mond[1 ] obtained sufficient and necessary optimality conditions andduality results.Reuda,Hanson[2 ] further extended type functions to pseu…     

Strong Time-Consistent Core for a Class of Linear-State Games

Time consistency is an important property of any solution to a cooperative dynamic game.If the solution satisfies this property, players do not need to revise it and break a cooperative agreement.Strong time consistency is a stricter property which is applicable to cooperative set solutions. In this paper, the authors examine a class of linear-state games which come into use in many applications of dynamic games. Considering the core as the solution of the game, the authors provide sufficient conditions for its strong time consistency. In case of its inconsistency, the authors show how core elements can be realized using a strong time-consistent imputation distribution procedure.     

Characteristic polynomial assignment in F-M model Ⅱ of 2-D systems

The problems of characteristic polynomial assignment in Fornasini-Marchesini (F-M) model Ⅱ of 2-D systems are investigated. The corresponding closed-loop systems described by F-M model Ⅱ are obtained via the state feedback.Using the algebraic geometry method, the characteristic polynomial assignment in the closed-loop systems is discussed. In terms of the theory of algebraic geometry, the problem of characteristic polynomial assignment is transferred to the one whether a rational mapping is onto. Sufficient conditions for almost arbitrary assignment coefficients of characteristic polynomial in F-M model Ⅱ of 2-D systems via state feedback are derived, and they are available for multi-input cases. It also has been shown that this method can be applied to assign the characteristic polynomial with output feedback. The sufficient conditions for almost arbitrary assignment coefficients of characteristic polynomial of multi-input 2-D systems described by F-M model Ⅱ with output feedback are established.     

The Influencing Factors of sCER Price Dynamics Under the Clean Development Mechanism: Theory and Econometric Analysis

In order to explore the factors and their complex mechanism affecting the price dynamics under the clean development mechanism(CDM), this article employs the secondary Certified Emission Reduction(sCER) carbon price as the study object, and analyzes its influencing factors from aspects of the international carbon-reduction policies, macroeconomic fluctuations, energy and similar carbon products prices. The innovation of this paper lies in: Introducing necessary factor(the developing countries pricing power) and the application of several international representative indicators to underline the "world" nature of CDM; utilizing different econometric models to obtain noteworthy and more robust results. The authors test the theoretical findings with multiple stationary time series from the launch of CDM to present(2008–2016). The results reveal that s CER price fluctuation shows the characteristic of asymmetry and substantial persistence. There is a strong statistically significant relationship between macroeconomic conditions, coal and oil prices, with the price of s CER. The authors discover that the pricing power of developing countries indeed has a clear but small impact on the s CER price changes, whereas the price elasticity of supply under CDM is so weak. The interaction between EU emission allowances(EUAs) and s CER presents a shift from dependency to substitution.     

Maximum likelihood estimator of the parameter for a continuous one-parameter exponential family under the optimal ranked set sampling

This paper studies a maximum likelihood estimator (MLE) of the parameter for a continuous one-parameter exponential family under ranked set sampling (RSS). The authors first find the optimal RSS according to the character of the family, viz, arrange the RSS based on quasi complete and sufficient statistic of independent and identically distributed (iid) samples. Then under this RSS, some sufficient conditions for the existence and uniqueness of the MLE, which are easily used in practice, are obtained. Using these conditions, the existence and uniqueness of the MLEs of the parameters for some usual distributions in this family are proved. Numerical simulations for these distributions fully support the result from the above two step optimizations of the sampling and the estimation method.     

Stochastic maximum principle for optimal control problems of forward-backward delay systems involving impulse controls

This paper is concerned with the optimal control problems of forward-backward delay systems involving impulse controls. The authors establish a stochastic maximum principle for this kind of systems. The most distinguishing features of the proposed problem are that the control variables consist of regular and impulsive controls, both with time delay, and that the domain of regular control is not necessarily convex. The authors obtain the necessary and sufficient conditions for optimal controls, which have potential applications in mathematical finance.     

CONTROLLABILITY OF EVOLUTION INCLUSIONS WITH NONLOCAL CONDITIONS

In this paper we examine controllability problems of evolution inclusions with nonlocal conditions. Using Kakutani‘s fixed point theorem and Schauder‘s fixed point the-orem, we establish sufficient conditions for the controllability under convex and nonconvex orientor fields respectively.